Motion-trail-like lines

A simple loop-based approach:

\documentclass[tikz,border=1cm]{standalone}
\usetikzlibrary{calc}
\begin{document}    

\begin{tikzpicture}[
    plotmark/.style = {%
    draw, fill=lightgray, circle, inner sep=0pt, minimum size=4pt
  }
]
\coordinate (A) at (0,0);
\coordinate (B) at (0,7);
\coordinate (C) at (7,5);
\coordinate (AnBC) at ($(B)!(A)!(C)$);

\draw (B)--(C);
\draw (A)--(AnBC);
\pgfmathtruncatemacro\parts{5}
\foreach \tikzi in {1,...,\parts} {
  \pgfmathtruncatemacro\colorspec{100-10*\tikzi}
  \draw[gray!\colorspec] (A) -- ($(AnBC)!\tikzi/\parts!(C)$);
}

\node[plotmark, label={below left:$A$}] at (A) {};
\node[plotmark, label={above left:$B$}] at (B) {};
\node[plotmark, label={above right:$C$}] at (C) {};

\end{tikzpicture}
\end{document}

TeXnician already told you the most important ingredient: a loop. Of course, one can define styles that use such loops. I followed your instructions on the syntax as far as I could, so you can do

 \draw[blue,set motion lines={lines=4,start opacity=0.2},rays=from A to line from C to AnBC];

MWE

\documentclass[tikz,border=1cm]{standalone}
\usetikzlibrary{calc}
\begin{document}    

\begin{tikzpicture}[
    plotmark/.style = {%
    draw, fill=lightgray, circle, inner sep=0pt, minimum size=4pt
  },rays/.style args={from #1 to line from #2 to #3}{insert path={
   foreach \X  in {0,...,\pgfkeysvalueof{/tikz/motion lines/lines}}
  {[/utils/exec=\pgfmathsetmacro{\myopa}{\pgfkeysvalueof{/tikz/motion lines/start opacity}
  +(\pgfkeysvalueof{/tikz/motion lines/end opacity}-\pgfkeysvalueof{/tikz/motion lines/start opacity})
  *\X/\pgfkeysvalueof{/tikz/motion lines/lines}}]
  (#1) edge[opacity=\myopa] ($(#2)!{\X/\pgfkeysvalueof{/tikz/motion lines/lines}}!(#3)$)}}},
  set motion lines/.code={\tikzset{motion lines/.cd,#1}},
  motion lines/.cd,
  lines/.initial=5,
  start opacity/.initial=0.1,
  end opacity/.initial=1,
  ]
 \coordinate (A) at (0,0);
 \coordinate (B) at (0,7);
 \coordinate (C) at (7,5);
 \coordinate (AnBC) at ($(B)!(A)!(C)$);
 \draw (B)--(C);
 \draw[dotted,rays=from A to line from C to AnBC];
 \node[plotmark, label={below left:$A$}] at (A) {};
 \node[plotmark, label={above left:$B$}] at (B) {};
 \node[plotmark, label={above right:$C$}] at (C) {};
 \begin{scope}[xshift=10cm]
  \coordinate (A) at (0,0);
  \coordinate (B) at (0,7);
  \coordinate (C) at (7,5);
  \coordinate (AnBC) at ($(B)!(A)!(C)$);
  \draw (B)--(C);
  \draw[blue,set motion lines={lines=4,start opacity=0.2},rays=from A to line from C to AnBC];
  \node[plotmark, label={below left:$A$}] at (A) {};
  \node[plotmark, label={above left:$B$}] at (B) {};
  \node[plotmark, label={above right:$C$}] at (C) {};
 \end{scope}
\end{tikzpicture}
\end{document}